{"id":"e-839c605163c8e6c6","operation":{"operation":"obreschkoff_combination"},"operation_detail":null,"conclusion_id":"n-8db14b5bac94a50b","premise_count":2,"theorem":"Hermite--Kakeya--Obreschkoff: real-rooted f, g with interlacing zeros give a zero or real-rooted a f + b g for all real a, b (Obreschkoff 1963; Fisk, Polynomials, roots, and interlacing, Thm 1.43)","lean_route":null,"lean_declarations":[],"certificate_hash":"272d97e0ceb3a805b57df2eb66de960cbbb559ed9d2878d3596e69408cfffc6b","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"obreschkoff_combination","certificate_raw_size":12220,"certificate_compressed_size":2696,"conclusion_name":"obreschkoff_combination of Triangle of 2-Eulerian numbers.","claims":[{"claim":"real_rooted","from_index":0,"region":{}}],"premises":[{"position":0,"node_id":"n-d2e17233522b2755","role":"sequence","name":"Triangle of 2-Eulerian numbers.","uses":{"claim":"real_rooted","from_index":0,"region":{}},"uses_text":"Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, +inf)"},{"position":1,"node_id":"n-d2e17233522b2755","role":"sequence","name":"Triangle of 2-Eulerian numbers.","uses":{"claim":"interlacing","from_index":1,"kind":"weak","orientation":"unordered"},"uses_text":"Rows P_(m-1), P_m interlace (weak, unordered) for every m >= 1"}],"cited_by":[{"node_id":"n-8db14b5bac94a50b","claim":"real_rooted"}]}